Foundations are a fundamental component of any structure, critically transmitting loads from the building to the underlying soil layers. Pile foundations are a category of deep foundations specifically designed to transfer loads through weaker soil strata to more stable, hard ground below.
The analysis of lateral loads is a crucial aspect of pile foundation design and engineering. When subjected to lateral loads, piles can exhibit complex behaviours, including bending and lateral displacement. Such
loads result from a variety of environmental factors, including seismic activity from earthquakes, forces generated by strong winds, or hydrodynamic effects from waves in coastal areas.
When lateral forces act on a single pile or a group of piles, they can induce rotations and bending moments, leading to significant deflections. Understanding the soil-pile interaction is essential when assessing how these lateral loads affect pile performance. This includes the determination of soil resistance as well as the behavior of the pile material under various loading conditions. Proper evaluation and reinforcement strategies are imperative to ensure structural integrity and safety, especially
in regions prone to dynamic environmental challenges.
Numerous studies have been undertaken by researchers worldwide, employing a variety of computational techniques such as genetic programming and artificial neural networks (ANN). One notable research effort was led by Pijush Samui et al., at VIT University in Vellore, who focused on determining the lateral load capacity of piles. This study utilized several advanced computational methodologies, including ANN, multivariate adaptive regression splines (MARS), and least squares support vector machines (LS-SVM).
Their findings were published in the esteemed journal Neural Computing and Applications in July 2012. This research contributes to the growing body of knowledge in geotechnical engineering by providing innovative approaches to predicting the behaviour of pile foundations under lateral loads.
Least Squares Support Vector Machine (LSSVM) is an advanced variation of the traditional support vector machine (SVM) algorithm. Unlike standard SVMs, which utilize inequality constraints, LSSVM employs equality constraints along with a least squares cost function. This approach not only simplifies the optimization problem but also results in a linear system of equations characterized by the Karush-Kuhn-Tucker (KKT) conditions. As a result, LSSVM can be more computationally efficient while still providing robust classification and regression capabilities.
On the other hand, Multivariate Adaptive Regression Splines (MARS) is a powerful nonparametric regression technique that uniquely does not assume a predetermined functional form between the independent and dependent variables. Instead, MARS constructs a piecewise linear model by adapting its
basis functions directly from the data set at hand. This flexibility allows MARS to capture complex nonlinear relationships and interactions within the data, making it an effective tool for modelling a wide variety of patterns without requiring explicit specifications of the underlying relationship.
The dataset utilized in this study comprises a total of 41 samples that were carefully selected to represent a range of conditions relevant to the analysis. To ensure a robust evaluation of the predictive models, the dataset was strategically divided into two distinct subsets: 70% of the samples were allocated for training the models, while the remaining 30% were reserved for testing their performance.
In the quest to accurately predict lateral loads exerted on pile foundations, a range of input parameters was employed. These parameters included the diameter of the pile (D), the depth at which the pile is embedded in the soil (L), the eccentricity of the applied load (e), and the undrained shear strength of the surrounding soil (Su). The selection of these variables is critical, as they encompass the essential factors influencing the behavior of pile foundations under lateral loading.
The modelling process was executed within the MATLAB environment, which provides a robust platform for data analysis and numerical modelling. To enhance the performance of the models, particularly the Least Squares Support Vector Machine (LSSVM) and Multivariate Adaptive Regression Splines (MARS), the hyperparameters were optimized through a thorough trial-and-error methodology. This iterative approach allowed for the fine-tuning of the models to better capture the underlying patterns in the
data.
The effectiveness of the developed models was evaluated using the correlation coefficient metric, R. Remarkably, both MARS and LSSVM outperformed the Artificial Neural Network (ANN) in terms of predictive accuracy, achieving R values of 0.995 and 0.994, respectively. These high values indicate a strong correlation between the predicted and observed lateral loads.
In conclusion, the implemented LSSVM and MARS models demonstrate significant potential as powerful tools for predicting the lateral loads acting on pile foundations, highlighting their relevance and utility in
geotechnical engineering applications.
Reference
Samui, P., Kim, D. Least square support vector machine and multivariate adaptive regression spline for modeling lateral load capacity of piles. Neural Comput & Applic 23, 1123–1127 (2013). https://doi.org/10.1007/s00521-012-1043-x